Loading…

On a smoothed penalty-based algorithm for global optimization

This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k , the framework requires the ε ( k ) -glob...

Full description

Saved in:
Bibliographic Details
Published in:Journal of global optimization 2017-11, Vol.69 (3), p.561-585
Main Authors: Rocha, Ana Maria A. C., Costa, M. Fernanda P., Fernandes, Edite M. G. P.
Format: Article
Language:English
Subjects:
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c423t-93a3d225f76a342554157c3a025a6dd31b168733575dae4f60913dd34b7e77823
cites cdi_FETCH-LOGICAL-c423t-93a3d225f76a342554157c3a025a6dd31b168733575dae4f60913dd34b7e77823
container_end_page 585
container_issue 3
container_start_page 561
container_title Journal of global optimization
container_volume 69
creator Rocha, Ana Maria A. C.
Costa, M. Fernanda P.
Fernandes, Edite M. G. P.
description This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k , the framework requires the ε ( k ) -global minimizer of a subproblem, where ε ( k ) → ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε ( k ) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε ( k ) -neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.
doi_str_mv 10.1007/s10898-017-0504-2
format article
fullrecord <record><control><sourceid>gale_proqu</sourceid><recordid>TN_cdi_proquest_journals_1953069465</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><galeid>A718416844</galeid><sourcerecordid>A718416844</sourcerecordid><originalsourceid>FETCH-LOGICAL-c423t-93a3d225f76a342554157c3a025a6dd31b168733575dae4f60913dd34b7e77823</originalsourceid><addsrcrecordid>eNp1kD1PwzAQhi0EEqXwA9giMbucv-JkYKgqvqRKXWC2nMRJXSVxsN2h_HpchYEF3XC60_vePXoRuiewIgDyMRAoygIDkRgEcEwv0IIIyTAtSX6JFlBSgQUAuUY3IRwAoCwEXaCn3ZjpLAzOxb1pssmMuo8nXOmQJt13ztu4H7LW-azrXaX7zE3RDvZbR-vGW3TV6j6Yu9--RJ8vzx-bN7zdvb5v1ltcc8oiLplmDaWilblmnArBE1rNNFCh86ZhpCJ5IRkTUjTa8DaHkrC055U0UhaULdHDfHfy7utoQlQHd_QJNShSCgZ5yXORVKtZ1eneKDu2Lnpdp2rMYGs3mtam_VqSgqd_nCcDmQ21dyF406rJ20H7kyKgzrGqOVaVYlXnWNUZhc6ekLRjZ_wflH9NP6R3eCo</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1953069465</pqid></control><display><type>article</type><title>On a smoothed penalty-based algorithm for global optimization</title><source>ABI/INFORM Global</source><source>Springer Link</source><creator>Rocha, Ana Maria A. C. ; Costa, M. Fernanda P. ; Fernandes, Edite M. G. P.</creator><creatorcontrib>Rocha, Ana Maria A. C. ; Costa, M. Fernanda P. ; Fernandes, Edite M. G. P.</creatorcontrib><description>This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k , the framework requires the ε ( k ) -global minimizer of a subproblem, where ε ( k ) → ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε ( k ) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε ( k ) -neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.</description><identifier>ISSN: 0925-5001</identifier><identifier>EISSN: 1573-2916</identifier><identifier>DOI: 10.1007/s10898-017-0504-2</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algorithms ; Coercivity ; Computer Science ; Convergence ; Fitness ; Global optimization ; Iterative methods ; Markov chains ; Markov processes ; Mathematics ; Mathematics and Statistics ; Nonlinear programming ; Operations Research/Decision Theory ; Optimization ; Penalty function ; Real Functions</subject><ispartof>Journal of global optimization, 2017-11, Vol.69 (3), p.561-585</ispartof><rights>Springer Science+Business Media New York 2017</rights><rights>COPYRIGHT 2017 Springer</rights><rights>Journal of Global Optimization is a copyright of Springer, 2017.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c423t-93a3d225f76a342554157c3a025a6dd31b168733575dae4f60913dd34b7e77823</citedby><cites>FETCH-LOGICAL-c423t-93a3d225f76a342554157c3a025a6dd31b168733575dae4f60913dd34b7e77823</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/1953069465/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$H</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/1953069465?pq-origsite=primo$$EHTML$$P50$$Gproquest$$H</linktohtml><link.rule.ids>314,780,784,11688,27924,27925,36060,44363,74895</link.rule.ids></links><search><creatorcontrib>Rocha, Ana Maria A. C.</creatorcontrib><creatorcontrib>Costa, M. Fernanda P.</creatorcontrib><creatorcontrib>Fernandes, Edite M. G. P.</creatorcontrib><title>On a smoothed penalty-based algorithm for global optimization</title><title>Journal of global optimization</title><addtitle>J Glob Optim</addtitle><description>This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k , the framework requires the ε ( k ) -global minimizer of a subproblem, where ε ( k ) → ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε ( k ) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε ( k ) -neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.</description><subject>Algorithms</subject><subject>Coercivity</subject><subject>Computer Science</subject><subject>Convergence</subject><subject>Fitness</subject><subject>Global optimization</subject><subject>Iterative methods</subject><subject>Markov chains</subject><subject>Markov processes</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear programming</subject><subject>Operations Research/Decision Theory</subject><subject>Optimization</subject><subject>Penalty function</subject><subject>Real Functions</subject><issn>0925-5001</issn><issn>1573-2916</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>M0C</sourceid><recordid>eNp1kD1PwzAQhi0EEqXwA9giMbucv-JkYKgqvqRKXWC2nMRJXSVxsN2h_HpchYEF3XC60_vePXoRuiewIgDyMRAoygIDkRgEcEwv0IIIyTAtSX6JFlBSgQUAuUY3IRwAoCwEXaCn3ZjpLAzOxb1pssmMuo8nXOmQJt13ztu4H7LW-azrXaX7zE3RDvZbR-vGW3TV6j6Yu9--RJ8vzx-bN7zdvb5v1ltcc8oiLplmDaWilblmnArBE1rNNFCh86ZhpCJ5IRkTUjTa8DaHkrC055U0UhaULdHDfHfy7utoQlQHd_QJNShSCgZ5yXORVKtZ1eneKDu2Lnpdp2rMYGs3mtam_VqSgqd_nCcDmQ21dyF406rJ20H7kyKgzrGqOVaVYlXnWNUZhc6ekLRjZ_wflH9NP6R3eCo</recordid><startdate>20171101</startdate><enddate>20171101</enddate><creator>Rocha, Ana Maria A. C.</creator><creator>Costa, M. Fernanda P.</creator><creator>Fernandes, Edite M. G. P.</creator><general>Springer US</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7WY</scope><scope>7WZ</scope><scope>7XB</scope><scope>87Z</scope><scope>88I</scope><scope>8AL</scope><scope>8AO</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>8FL</scope><scope>8G5</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BEZIV</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FRNLG</scope><scope>F~G</scope><scope>GNUQQ</scope><scope>GUQSH</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K60</scope><scope>K6~</scope><scope>K7-</scope><scope>L.-</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0C</scope><scope>M0N</scope><scope>M2O</scope><scope>M2P</scope><scope>M7S</scope><scope>MBDVC</scope><scope>P5Z</scope><scope>P62</scope><scope>PQBIZ</scope><scope>PQBZA</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope></search><sort><creationdate>20171101</creationdate><title>On a smoothed penalty-based algorithm for global optimization</title><author>Rocha, Ana Maria A. C. ; Costa, M. Fernanda P. ; Fernandes, Edite M. G. P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c423t-93a3d225f76a342554157c3a025a6dd31b168733575dae4f60913dd34b7e77823</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algorithms</topic><topic>Coercivity</topic><topic>Computer Science</topic><topic>Convergence</topic><topic>Fitness</topic><topic>Global optimization</topic><topic>Iterative methods</topic><topic>Markov chains</topic><topic>Markov processes</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear programming</topic><topic>Operations Research/Decision Theory</topic><topic>Optimization</topic><topic>Penalty function</topic><topic>Real Functions</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Rocha, Ana Maria A. C.</creatorcontrib><creatorcontrib>Costa, M. Fernanda P.</creatorcontrib><creatorcontrib>Fernandes, Edite M. G. P.</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Computer and Information Systems Abstracts</collection><collection>ProQuest_ABI/INFORM Collection</collection><collection>ABI/INFORM Global (PDF only)</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection</collection><collection>Science Database (Alumni Edition)</collection><collection>Computing Database (Alumni Edition)</collection><collection>ProQuest Pharma Collection</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>ABI/INFORM Collection (Alumni Edition)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science &amp; Engineering Collection</collection><collection>ProQuest Central (Alumni)</collection><collection>ProQuest Central</collection><collection>Advanced Technologies &amp; Aerospace Database‎ (1962 - current)</collection><collection>ProQuest Central Essentials</collection><collection>AUTh Library subscriptions: ProQuest Central</collection><collection>ProQuest Business Premium Collection</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central</collection><collection>Business Premium Collection (Alumni)</collection><collection>ABI/INFORM Global (Corporate)</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Computer Science Collection</collection><collection>ProQuest Business Collection (Alumni Edition)</collection><collection>ProQuest Business Collection</collection><collection>Computer science database</collection><collection>ABI/INFORM Professional Advanced</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts – Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ABI/INFORM Global</collection><collection>Computing Database</collection><collection>ProQuest_Research Library</collection><collection>ProQuest Science Journals</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>ProQuest advanced technologies &amp; aerospace journals</collection><collection>ProQuest Advanced Technologies &amp; Aerospace Collection</collection><collection>One Business (ProQuest)</collection><collection>ProQuest One Business (Alumni)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><collection>Engineering collection</collection><collection>ProQuest Central Basic</collection><jtitle>Journal of global optimization</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Rocha, Ana Maria A. C.</au><au>Costa, M. Fernanda P.</au><au>Fernandes, Edite M. G. P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On a smoothed penalty-based algorithm for global optimization</atitle><jtitle>Journal of global optimization</jtitle><stitle>J Glob Optim</stitle><date>2017-11-01</date><risdate>2017</risdate><volume>69</volume><issue>3</issue><spage>561</spage><epage>585</epage><pages>561-585</pages><issn>0925-5001</issn><eissn>1573-2916</eissn><abstract>This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k , the framework requires the ε ( k ) -global minimizer of a subproblem, where ε ( k ) → ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε ( k ) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε ( k ) -neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s10898-017-0504-2</doi><tpages>25</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0925-5001
ispartof Journal of global optimization, 2017-11, Vol.69 (3), p.561-585
issn 0925-5001
1573-2916
language eng
recordid cdi_proquest_journals_1953069465
source ABI/INFORM Global; Springer Link
subjects Algorithms
Coercivity
Computer Science
Convergence
Fitness
Global optimization
Iterative methods
Markov chains
Markov processes
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Penalty function
Real Functions
title On a smoothed penalty-based algorithm for global optimization
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T11%3A16%3A48IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-gale_proqu&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20a%20smoothed%20penalty-based%20algorithm%20for%20global%20optimization&rft.jtitle=Journal%20of%20global%20optimization&rft.au=Rocha,%20Ana%20Maria%20A.%20C.&rft.date=2017-11-01&rft.volume=69&rft.issue=3&rft.spage=561&rft.epage=585&rft.pages=561-585&rft.issn=0925-5001&rft.eissn=1573-2916&rft_id=info:doi/10.1007/s10898-017-0504-2&rft_dat=%3Cgale_proqu%3EA718416844%3C/gale_proqu%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c423t-93a3d225f76a342554157c3a025a6dd31b168733575dae4f60913dd34b7e77823%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_pqid=1953069465&rft_id=info:pmid/&rft_galeid=A718416844&rfr_iscdi=true